An infinite geometric series has common ratio $1/8$ and sum 60.  What is the first term of the series?
Solution: Let the first term be $a$.  Because the sum of the series is 60, we have  $$60= \frac{a}{1-(1/8)} = \frac{a}{7/8} = \frac{8a}{7}.$$Therefore, $a=\frac{7}{8}\cdot60=\boxed{\frac{105}{2}}$.